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Hint: Ask Aristotle. And .

Facebook’s (NASDAQ:FB) acquisition of WhatsApp for a whopping $19 billion dollars demonstrates the company’s determination to remain the leader in social networking, even if that comes at a hefty premium.

At the same time, it reveals a very important limitation in Facebook’s business model: the very assumption that everyone can be a friend with everyone else.

Long before Mark Zuckerberg created Facebook, Aristotle has argued that “true” friendship is governed by a strictly qualitative logic. That is, friendship is a rare spiritual intimacy that can only be shared among a handful of people.

As a result, a person may live an entire life and only possess three or four “real” friends.

Some people assume they are blessed because they can name fifty or sixty individuals whom they designate as friends. In truth, numbers such as these indicate neither good fortune nor extraordinary popularity, but a complete misunderstanding of genuine friendship.

Friendship shouldn’t be confused with pseudo-friendship, or “utility relationships” which fade away as soon as the “utility” is no longer there, as discussed in a previous piece.

That could explain why people are turning from noisy networks to the smartphone book. “Weary of noisy social networks filled with mundane updates from the most remote acquaintances, millions of people have turned to their smartphone address books—and the diverse array of messaging services that rely on them, like Snapchat, Secret, Kik and WhatsApp—for more intimate connections,” writes Jenna Wortham of New York Times. “Facebook has long defined the digital social network, and the average adult Facebook user has more than 300 friends. The company’s strategy has mostly been about making that circle of friends even bigger, cajoling users into combining their friends, former friends, co-workers, second cousins and everyone they’ve ever met into a single, ballooning social network.”

To be fair, people still have a need for connection and communication with other members of society. But that’s where other social networks like and Twitter come into play.

I personally feel more comfortable adding people I know professionally to my LinkedIn network and Twitter accounts than my Facebook account.

What does all this mean for the future of Facebook’s acquisition of WatsApp and the hefty premium paid?

In the short-term, it is positive for the new company, creating good synergies between the acquirer and the acquired. And it places Facebook a step ahead of the competition.

That could explain why investors, skeptical at first, eventually endorsed the deal, moving Facebook’s shares higher.

But can Facebook keep on paying a hefty premium for every upstart that challenges its market dominance? That’s a question Facebook should ask Cisco Systems -- which has followed a similar strategy.

As we wrote in previous pieces, this strategy isn’t sustainable. Owners of these smaller companies demand higher and higher premium to compensate them for the risks they assume — Cisco end up paying top prices for Net Speed and Growth Networks acquired at the peak of the high-tech bubble.